We investigate the interactions between a cantilevered flexible beam and cross-flow of a viscoelastic fluid. Unlike Newtonian fluids, viscoelastic fluids exhibit elastic flow instabilities even in the absence of inertia. These elastic flow instabilities drive the oscillations of flexible structures placed in their flow path. In this work, the fluid–structure interactions between the flow of viscoelastic wormlike micelle solution and a flexible cantilevered beam is studied as a function of the Weissenberg number and the beam’s tip angle. At low Weissenberg numbers, the flow remained stable and the beam deflected in the direction of flow. As the Weissenberg number was increased, a separated vortex appeared upstream of the cantilever near its tip. At a critical Weissenberg number of $Wi=11$, the flow became unstable. For beams with small tip angles of 0° and 25°, no oscillations were observed. However, for beams with larger tip angles of 45° and 65°, oscillatory motions coupled to the flow instability were observed, where the amplitude of the beam oscillations increased with increasing tip angle. Particle image velocimetry measurements showed that the elastic flow instability was characterized by the periodic formation of strong fluid jet that originated upstream of the beam in a region of strong extensional flow where it likely resulted from the local breakdown of the wormlike micelle solution. This jet was accompanied by a pair of counter-rotating vortices on its sides as it entrained fluid around the tip of the beam. The frequency of oscillations of the beams with large tip angles increased monotonically with Weissenberg number, while their amplitudes of oscillations initially increased with Weissenberg number before decaying to zero for $Wi>20$, despite the fact that the flow remained unstable. Our results showed that oscillations were only possible when the tip of the cantilevered beam made a positive angle with respect to the primary incoming flow direction.

我们研究悬臂挠性梁和粘弹性流体的横流之间的相互作用。与牛顿流体不同，粘弹性流体即使在没有惯性的情况下也表现出弹性流动不稳定性。这些弹性流动不稳定性驱动放置在其流动路径中的柔性结构的振动。在这项工作中，研究了粘弹性蠕虫状胶束溶液与柔性悬臂梁之间的流固耦合，它是Weissenberg数和梁顶角的函数。在较低的魏森伯格数下，流量保持稳定，并且光束沿流向偏转。随着魏森伯格数的增加，在悬臂顶端附近出现了一个分离的涡流。Weissenberg处于临界状态$\mathrm{w\; ^}\mathrm{一世}=11$，流量变得不稳定。对于小倾角为0°和25°的光束，未观察到振荡。但是，对于具有45°和65°较大尖端角的光束，观察到与流动不稳定性相关的振荡运动，其中光束振荡的幅度随尖端角的增加而增加。颗粒图像测速仪的测量结果表明，弹性流动的不稳定性具有周期性形成的强流体射流的特征，该射流起源于束流上游的强延伸流区域，这可能是由于蠕虫状胶束溶液的局部破坏所致。这股射流在其侧面伴随着一对反向旋转的涡流，因为它围绕着射束的尖端夹带了流体。尖角大的光束的振荡频率随魏森贝格数单调增加，$\mathrm{w\; ^}\mathrm{一世}>20$，尽管流量仍然不稳定。我们的结果表明，仅当悬臂梁的尖端相对于主要进入流向成正角时才可能发生振荡。